How many data points needed before a nonlinear regression model can be performed?

With a within-subject design of only one independent variable, I'm wondering how many data points (levels of the indept variable along X axis) do I need before I could attempt to do a nonlinear regression of my data. Each data point would be the average of all subjects' measurements on that level of independent variable.

Nonlinear regression is preferred because I'd like to characterize the relationship between the dependent and independent variables.

Any thoughts would be appreciated! I posted a similar question in the stats research forum but didn't get any replies. I thought rewording and posting in the regression forum might help. Sorry for the double-posting!

Link asks a good question. A lot of times when people think they want to do nonlinear regression it still falls in the realm of a linear model.

I'm wondering why you're averaging the datapoints though. It's typically better to leave the raw data as is and model the correlations between datapoints inside the model. Sometimes it's alright to average but you don't have to.

Link asks a good question. A lot of times when people think they want to do nonlinear regression it still falls in the realm of a linear model.

I'm wondering why you're averaging the datapoints though. It's typically better to leave the raw data as is and model the correlations between datapoints inside the model. Sometimes it's alright to average but you don't have to.

I was thinking nonlinear because the hypothesized behaviour for my data would be something that looks like a negative exponential function y=a-b*c^x (or a rational function) that approaches a horizontal asymptote after increasing initially. The premise of the study is hard to explain in a few words, but basically I'm expecting to see some kind of diminishing return after a certain level in X (independent var). It might be a matter of transforming the data first and then looking for a linear regression fit. I am not sure which. Does the choice of linear vs. nonlinear regression affect the data points needed?

Dason, I was also pondering whether or not I should average the data. After what you said here I am leaning on the side of not averaging the data. Would this solve my problem of too few data points for modeling purpose?